Cofiniteness of modules and local cohomology

Abstract

Let $A$ be a commutative noetherian ring, let $\mathfrak{a}$ be an ideal of $A$ and let $n$ be a non-negative integer. In this paper, we study ${\mathcal{S}}_n(\mathfrak{a})$, a certain class of $A$-modules and we find some sufficient conditions so that a module belongs to ${\mathcal{S}}_n(\mathfrak{a})$. Moreover, we study the cofiniteness of local cohomology modules when $\dim A/\mathfrak{a}\ge 3$.